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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2403.17952 |
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| _version_ | 1866916181838921728 |
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| author | Pan, Ende Xu, Ce |
| author_facet | Pan, Ende Xu, Ce |
| contents | In this paper, we establish some expressions of Mneimneh-type binomial sums involving multiple harmonic-type sums in terms of finite sums of Stirling numbers, Bell numbers and some related variables. In particular, we present some new formulas of Mneimneh-type binomial sums involving generalized (alternating) harmonic numbers. Further, we establish a new identity relating the multiple zeta star values $ζ^\star(m+2,\{1\}_{r-1})$ and specific multiple polylogarithms by applying the Toeplitz principle. Furthermore, we present some interesting consequences and illustrative examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_17952 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Mneimneh-type Binomial Sums of Multiple Harmonic-type Sums Pan, Ende Xu, Ce Number Theory In this paper, we establish some expressions of Mneimneh-type binomial sums involving multiple harmonic-type sums in terms of finite sums of Stirling numbers, Bell numbers and some related variables. In particular, we present some new formulas of Mneimneh-type binomial sums involving generalized (alternating) harmonic numbers. Further, we establish a new identity relating the multiple zeta star values $ζ^\star(m+2,\{1\}_{r-1})$ and specific multiple polylogarithms by applying the Toeplitz principle. Furthermore, we present some interesting consequences and illustrative examples. |
| title | Mneimneh-type Binomial Sums of Multiple Harmonic-type Sums |
| topic | Number Theory |
| url | https://arxiv.org/abs/2403.17952 |